By Marilyn Dubinski / Pounding The Rock, 2026-11-12 23:43:32
有一种流行的说法叫做“平均法则”。虽然它并非数学界公认的定理，但作为一种俗语，它指的是：如果某件事发生的频率高于或低于它应有的水平，逻辑告诉我们，事情最终会回归平衡、恢复正常。这在赌博界是个谬误；如果你一直抛硬币，它一直落在反面，这并不意味着下一次落在正面的概率会更大，因为每一次抛掷都是独立事件，彼此之间没有关联。同样，如果你每次都重新开一局纸牌游戏、用一副完整的新牌——你赢的概率并不会因为距离上次赢已经过了很久就有所提高，因为这一手牌和上一手没有任何关系。
然而，平均法则以及与之相伴的“定律”确实经常适用的一个领域是篮球。虽然从技术上讲这仍是数学上的谬误，但体育运动最重要的归根结底是天赋，而在大样本下，数据确实能说明问题。当然，每场单独的比赛彼此是独立事件，但同样的球员带着同样的技能做着同样的动作，所以这些独立事件之间确实存在关联，而且大多数情况下，他们的表现会接近数据所预示的水平。
当然，总会有异常值和意外事件——如果一切都按预期发展，体育就没那么有意思了——而这正是昨晚圣安东尼奥马刺与芝加哥公牛上半场发生的情况。马刺此前处于九连胜，对手的赛程强度大家大概都能承认算不上最难，但考虑到对手正处于七连败，这很可能是一场“陷阱比赛”，而平均法则说，其中一个连胜/连败纪录总该接近终结了吧？这也是四连客的最后一场，这趟客场之旅一切太顺利了，他们可能已经在惦记周五对阵勇士的杯赛了（如果斯蒂芬·库里在昨晚对阵火箭的比赛中腹部受伤后缺阵，那场比赛的看点可能会打些折扣）。
除了达龙·福克斯 (De’Aaron Fox) 的一波三分雨和火热开局短暂让他们保持竞争力之外，马刺很快发现自己落后了，而公牛在比赛前18分钟里手感热得发烫。他们第一节投篮17投20中（命中率85%），第二节某一时刻投篮和三分命中率都达到了83%。虽然马刺的努力程度谈不上令人钦佩，但我在上半场从未太过担心，因为我知道平均法则终将发挥作用。
没有任何球队，即使是十年前的勇士，能在一整场比赛中维持那种数据，更不用说像公牛这样糟糕的球队了。他们在上半场将领先优势扩大到22分，但马刺顶住了风暴，等待着自己的数据回归平均值，同时知道自己还有另一个档位可以开启。他们利用半场前的一波攻势将分差缩小到非常可控的14分，同时公牛的数据开始下滑（到半场结束时他们“仅”有67%的命中率），在更衣室里接受了米奇·约翰逊 (Mitch Johnson) 理所当然的一顿训斥，然后下半场火力全开。
随着马刺恢复正常状态，公牛理所当然地被压制了，他们知道自己已经打出了最好的表现，而平均法则现在已经生效。维克托·文班亚马 (Victor Wembanyama) 重新以不可阻挡的篮下存在感摧毁对手的士气，同时在进攻流畅运转中适时出手（并命中）跳投，保持了平衡。到比赛结束时，一切都回到了应有的样子：马刺以50%的投篮命中率（三分38%）获胜，而公牛虽然凭借超凡的上半场最终数据依然亮眼（分别为58%和52%），但他们的运动战进球少了5个，部分原因是他们出现了19次失误，而马刺只有6次。平均法则在马刺的第十场连胜中依然生生不息。
或者，你知道的，也许这跟平均法则毫无关系，只是公牛主场的篮筐有什么问题。你完全可以在看完那场比赛后简单地得出结论：根据两队上下半场投篮的巨大波动来看，“右边篮筐好，左边篮筐差。”
要点
- “哦，文班18投13中得了32分，还有9个篮板和5次盖帽？平平无奇，又一个工作日罢了。”是的，我们已经到了对他这种表现习以为常的地步。他最近的数据太离谱、甚至堪称历史级别，以至于我昨晚几乎都没怎么注意到他。看着对方球迷惊叹连连确实很有趣，而我们只是，“他从罚球线扣篮了？没什么新鲜的。”
- 你知道还有什么能说明一个人已经达到伟大境界吗？当黑子开始黑的时候。“他7尺7寸，要有低位技术才能伟大！”文班开始在禁区统治：“那又怎样？他只是长得高！”我最近看到的最搞笑的“愤怒”推文是一个人抱怨他“只能”打25分钟，所以身体状态肯定不好。不是的兄弟，那只是因为比赛经常打花，他不需要打更多时间。如果他真在垃圾时间刷数据，你又会指责他刷数据了。正如老话所说，“黑子尽管黑，马刺尽管赢”。
- 我觉得现在是时候把福克斯总决赛的糟糕表现翻篇了。我们都知道他当时是一条腿在打球，虽然他犯了几个重大失误，但他不是唯一犯错或导致系列赛失利的人；那是全队的责任。（我甚至在昨天一条Feed帖子下的评论中指出，如果总决赛打得更久，文班就会像德雷蒙德·格林 (Draymond Green) 一样在履历上留下污点，因为他极有可能因恶意犯规累计而在第六场被禁赛——而且那还是在第三场侥幸逃过之后。联盟不会两次救他。）但回到福克斯，对于这支仍然年轻的球队来说，他一直是一个极其稳定的存在，目前斯蒂芬·卡斯尔 (Stephon Castle) 状态有些低迷，迪伦·哈珀 (Dylan Harper) 整体打得很好但每节之间仍有起伏。是时候重新记住并感激福克斯带来的好处了，这些远远超过了一只伤脚踝上的几次糟糕表现。
- 马刺赛季开局赛程强度也许不是最强的，但确实令人疲惫，至少对我来说是这样。前十场里有三次背靠背，前20场中有12场开球时间在晚上8点或更晚——这对我的睡眠作息简直是折磨。这就是为什么昨晚7点的开球时间感觉太棒了。我看了比赛，比赛结束了，然后我在正常时间（或者说现在感觉算早的时间）上床睡觉，周四早上还算精神。好消息是，第20场之后——黑色星期五晚上8点半对阵湖人——马刺直到1月20日第42场（从欧洲之旅回来的第一场）之前，都不会再有开球时间晚于7点的比赛了。
由生成式 AI 翻译，翻译内容可能不准确或不完整，以原文为准。
查看原文：What we learned from the Spurs win over the Bulls
What we learned from the Spurs win over the Bulls
There’s this popular belief known as the Law of Averages. While it’s not a recognized theorem in the mathematical world, it’s a common saying that refers to the idea that if something happens more or less often than it should, logic says things will eventually balance back out and return to normal. It’s a fallacy in the gambling world; if you keep flipping a coin and it keeps landing on tails, that doesn’t mean the odds are better it will land on heads the next time because each individual flip is a separate event with no relationship to another. The same applies if you keep starting a card game over with a full or new deck — your odds of winning don’t improve just because it’s been a while since you last won, because this hand has no relationship to the last.
However, one place where averages and the “laws” that go with them do often apply is basketball. While still technically a mathematical fallacy, one thing about sports is more than anything, it comes down to talent, and across a large sample size, the numbers do in fact tell a story. Sure, each individual game is a separate event from each other, but it’s the same players with the same skillset going through the same motions, so there is in fact a relationship across the separate events, and more often than not, they will do close to what the numbers say they will.
Of course, there are always outliers and unexpected events — sports wouldn’t be any fun if everything always went as expected — and that’s exactly what happened last night in the first half between the San Antonio Spurs and Chicago Bulls. The Spurs were on a nine-game winning against what we can all probably admit is not the most difficult stretch of schedule ever, but they were walking into a potential trap game considering it was against a team on a seven-game losing streak, and the Law of Averages says one of those streaks is getting closer to ending, right? It was also the end of a four-game road trip, things have been too easy on said-trip, and they may have been looking ahead to Friday’s Cup match against the Warriors (which may have lost some luster if Steph Curry is out after appearing to injure his abdomen last night against the Rockets).
Other than a flurry from three and a hot start from De’Aaron Fox briefly keeping them in it, the Spurs quickly found themselves falling behind while the Bulls were insanely hot through the first 18 minutes of the game. They shot 17-20 (or 85%) from the field in the first quarter and at one point were shooting 83% from both the field AND three in the second. While the Spurs’ effort wasn’t what you’d call admirable, I was never too worried during the first half because I knew the Law of Averages would eventually take over.
No team, not even the Warriors of a decade ago, can keep up those types of numbers for an entire game, let alone a team as bad as these Bulls. They got the lead as high as 22 in the first half, but the Spurs weathered the storm and waited for their numbers to start averaging back to the mean while knowing they had a another gear they could turn on. They used a run before halftime to cut the deficit to a very manageable 14 points while the Bulls’ numbers starting dropping (they were “only” shooting 67% by the midway mark), took their presumed licking from Mitch Johnson in the locker room, then came out firing in the second half.
As the Spurs returned to their normal selves, the Bulls were understandably overwhelmed, knowing they had already given their best shot and the Law of Averages had now taken its hold. Victor Wembanyama went back to demoralizing teams with an unstoppable presence at the rim, balanced out by taking (and making) timely jumpers within the flow of the offense. By the end of the game, everything was as it should be: the Spurs won while shooting 50% from the field (38% from three), and while the Bulls still ended with impressive final numbers (58% and 52%, respectively) thanks to their otherworldly first half, they made five fewer field goals thanks in part to coughing the ball up 19 times compared to the Spurs’ 6. The Law of Averages was alive and well for the Spurs 10th straight victory.
Or, you know, maybe that had nothing to do with it at all and there was just something off with the Bulls’ court. You could have watched that game and simply concluded that, based on the massive swings in shooting each team took from half-to-half, “Right rim good, left rim bad.”
Takeaways
- “Oh, Wemby had 32 points on 13-18 shooting, 9 rebounds and 5 blocks? Ho hum, just another day at the office.” Yes, we have reached that point with him. His numbers have been so outlandish and even historical lately that I hardly even noticed him last night. And while it’s fun to see opposing fans oohing and awing, we’re just like, “He dunked from the free throw line? Nothing new.”
- You know how else you know someone has arrived at greatness? When the haters start hating. “He’s 7’7”, he should have a post game to be great!” Wemby starts dominating in the paint: “So what? He’s just tall!” The funniest “rage” tweet I saw recently was one dude complaining that he can “only” handle 25 minutes per game, so he must not be in good shape. No bro, that’s just a result of all the blowouts and him not needing any more minutes. And if he was playing into extended garbage time, you’d just accuse him of stat padding. As the old saying goes, “Haters gonna hate, Spurs gonna win”.
- I think it’s officially time that we put Fox’s poor finals performance behind us. We all know he was playing on one leg, and while he had a couple of massive gaffes, he wasn’t the only one who messed up or cost them the series; it was a team effort. (I even pointed out in a comment on a Feed post yesterday that had the Finals gone any further, Wemby would have a Draymond Green mark on his legacy because he more than likely would have been suspended for Game 6 for flagrant accumulation — and that was after he was lucky to avoid it after Game 3. The league wasn’t going to bail him out twice.) But back to Fox, he has been a tremendous steadying present for this still-young squad, with Stephon Castle in a bit of a funk right now and Dylan Harper playing very well overall but still streaky from quarter to quarter. It’s time we get back to remembering and appreciating the good Fox brings, which far outweighs a couple of bad plays on a bum ankle.
- The strength of schedule of the Spurs’ start to the season may not be the strongest, but it has been exhausting, at least for me. Three back-to-backs in the first 10 games, 12 of the first 20 with tip-off times at 8:00 or later — it’s been brutal for my sleep schedule. That’s why last night’s 7:00 tip-off time was the most amazing feeling ever. I watched, it ended, then I went to bed at my normal time (or what now feels early), and I’m relatively fresh for a Thursday morning. The good news is after game 20 — 8:30 against the Lakers on Black Friday — the Spurs won’t have another game with a tip-off time later than 7 until #42 on January 20: their first game back from the Europe trip.
By Marilyn Dubinski / Pounding The Rock
热评